Question

Question 4 – ALL CALCULATIONS MUST BE SHOWN

The daily market demand for bananas is P=20-0.01Q and the daily market supply of bananas is P=2+0.02Q where P is the price in dollars per kilogram and Q is thousands of kilograms of bananas.

a. Suppose the market price of bananas is regulated at $10 per kilogram. Explain what type of policy this is and whether it is intended to assist banana producers or consumers.

b. What will be the quantity of bananas demanded at the regulated price?

c. What will be the quantity of bananas supplied at the regulated price?

d. Illustrate on a demand and supply diagram the changes in areas of economic surplus resulting from the regulated price.

Answer 1

Daily market demand for bananas: P=20-0.01Q

Daily market supply of bananas: P=2+0.02Q

(a) So, first lets find out the equilibrium price and quantity, to find them we have to equate the market demand for bananas with the market supply of bananas.

20 - 0.01Q = 2 + 0.02Q

or, 20 - 2 = 0.02Q + 0.01Q

or, 18 = 0.03Q

or, Q = 18 / 0.03

or, Q = 600 Kilogram

P = 20 - 0.01Q

or, P = 20 - 0.01(600)

or, P = 20 - 6

or, P = $ 14 per kilogram

Now, if the market price of bananas is regulated at $10 per kilogram i.e. the price is less than the market equilibrium price, this policy is a price ceiling. The government controls the prices of some products from reaching too high so that most of the consumers can afford to buy that product. So, Price ceiling is meant to protect consumers and it is mainly imposed on such products which are essentials like food products so that the poor people of the country can consume it at a lower price.

(b) The regulated price is $10 per kilogram.

So, the quantity of bananas demanded at the regulated price is:

Daily market demand for bananas: P=20-0.01Q

10 = 20 - 0.01 Q

0.01 Q = 20 - 10

Q = 10 / 0.01

Q = 1,000

(c) The quantity of bananas supplied at the regulated price is:

P = 2+0.02 Q

10 = 2 + 0.02 Q

8 = 0.02 Q

Q = 8 / 0.02

Q = 400

(d) The changes in areas of economic surplus resulting from the regulated price:

In the diagram below CS = Consumer Surplus, PS = Producer Surplus and E = Equilibrium Point.

Economic Surplus = Producer Surplus + Consumer Surplus

In the first diagram the initial Consumer Surplus and the initial Producer Surplus is shown. The Consumer Surplus is the area above the equilibrium price and the Producer Surplus is the area below the equilibrium price.

In the second diagram the final Consumer Surplus and the final Producer Surplus is shown after the imposition of price ceiling. We see that the Consumer Surplus has increased in area after the price ceiling and the producer surplus has decreased in area after the price ceiling.